How can I increase the darkness of shadows without increasing the strength of the lamp?
Perhaps it's possible using the Shadow output of the Lightpath node but I couldn't do it. 
What I could do, is enable the Shadow pass tick box in the Render Layers panel and then use that shadow pass to darken the shadows of the render with a mix(darken) node. Use a very small factor though as darken can be very intense.
Hope this helps you.